{"paper":{"title":"Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI"],"primary_cat":"cs.DS","authors_text":"Hong Shen, Kewen Liao, Longkun Guo","submitted_at":"2013-01-22T04:52:06Z","abstract_excerpt":"For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\\in Z^{+}$ and delay bound $D\\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \\cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\\beta,\\,\\max\\{2,\\,1+\\ln\\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5070","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}